Problem: Luis is 5 times as old as William. Six years ago, Luis was 7 times as old as William. How old is William now?
Explanation: We can use the given information to write down two equations that describe the ages of Luis and William. Let Luis's current age be $l$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $l = 5w$ Six years ago, Luis was $l - 6$ years old, and William was $w - 6$ years old. The information in the second sentence can be expressed in the following equation: $l - 6 = 7(w - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to use our first equation for $l$ and substitute it into our second equation. Our first equation is: $l = 5w$ . Substituting this into our second equation, we get: $5w$ $-$ $6 = 7(w - 6)$ which combines the information about $w$ from both of our original equations. Simplifying the right side of this equation, we get: $5 w - 6 = 7 w - 42$ Solving for $w$ , we get: $2 w = 36.$ $w = 18$.